The two clubs are understood to have moved closer together on a deal for the 21-year-old Senegal international, with the fee reported to be worth close to £40million — potentially double the amount West Ham paid Slavia Prague for him just over a year ago.
Diouf made 32 appearances for West Ham last season as they were relegated to the Championship, and played in the club's Championship opener, a 2-2 draw against Burnley. He was left out of the squad entirely, however, for the weekend's 2-1 defeat at Charlton Athletic, a decision that fuelled speculation his move to Brentford was drawing closer.
A switch to Brentford would take Diouf to a west London rival who have started life back in the Premier League in impressive fashion, having beaten Tottenham Hotspur 3-0 in their season opener.
Keane Lewis-Potter played at left-back in that victory and scored one of the goals, meaning Diouf would face immediate competition for his best position should the move go through.
Diouf's underlying numbers marked him out as one of the Championship's better attacking full-backs last season despite West Ham's struggles, contributing five assists across more than 2,700 minutes and featuring for Senegal at this summer's World Cup.
West Ham United, who have already banked significant funds from player sales this summer, would stand to make a considerable profit on a player signed for closer to £20million only 12 months ago.
Brentford have already had a busy window in their own right, breaking their transfer record to sign midfielder Mamadou Sangaré from Lens, and also bringing in Jaidon Anthony, Jannik Schuster and former Newcastle United striker Callum Wilson.
A move for Diouf would represent a further show of ambition from Keith Andrews's side as they attempt to build on their eye-catching start to the campaign, with the club having already seen off competition from elsewhere in the Premier League for the defender's signature this summer.